Abstract

In this methodological paper we consider geodesic motion of particles in spherically symmetric black hole space-times.We develop an approach based on splitting the velocity of a freely falling particle to the flow velocity, which depends only on the metric, and a deviation from it (a peculiar velocity). It applies to a wide class of spherically symmetric metrics and is exploited under the horizon of the Schwarzschild black hole. The present work generalizes previous results obtained for pure radial motion. Now, the motion is, in general, nonradial, so that an observer can have a nonzero angular momentum. This approach enables us to give simple physical interpretation of redshifts (blueshifts) inside the horizon including the region near the singularity and agrees with the recent results obtained by direct calculations.

中文翻译：

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球对称黑洞中一般运动的流动和特殊速度

摘要

在这篇方法论论文中，我们考虑了球对称黑洞时空中粒子的测地线运动。 我们开发了一种基于将自由下落粒子的速度分裂为流速的方法，该方法仅取决于度量，以及与它的偏差（一种特殊的速度）。它适用于范围广泛的球对称度量，并在 Schwarzschild 黑洞的视界下被利用。目前的工作概括了以前对纯径向运动获得的结果。现在，运动通常是非径向的，因此观察者可以具有非零角动量。这种方法使我们能够对视界内的红移（蓝移）进行简单的物理解释，包括奇点附近的区域，并与最近通过直接计算获得的结果一致。